Make particule collection retain keyframed movement
Try changing the Particle Settings
I went through this tutorial today and ran into your question when I was following the same steps and seeing that my Collection of &quot;People&quot; were only moving forward in the collection, and not as Particles.

I wanted to make sure to check the same things I went through to solve the issue:

Under the Collection of the Particle Settings
Checking the box Whole Collection changed my particles to move like they were in the collection, rather than just marching in place


Hope this helps any who see it, checking this box wasn't in the tutorial as I know.
Not certain this is the proper fix but this is from the documentation:

Whole Collection
Use the whole group at once, instead of one of its elements, the group
being displayed in place of each particle.

from Blender API